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Sorry, but I feel the need to correct The Black Empoleon. If you are mentioning Pokemon Amie, then you must be referring to the 6th Gen games. In the 6th Gen, Pokemon naturally have 1/8 chance to critical hit (doubled from the previous games), however there is reduced damage (1.5 instead of 2) to compensate for this chance increase. Therefore, if having Max Affection doubles your chance (like other Crit Rate boosting items, abilities or moves) then it would work out that a Max Affection Absol w/Pressure would have 1/4 chance to Critical Hit per attack, the same as a standard Super Luck Absol. In this case, we could have a Max Affection Super Luck Absol with a 1/2 Chance to critical hit, add a high Crit Rate move like Night-Slash, or a Razor Claw and you will always get Critical Hits (100% chance). In this case, Razor Claw would be better than Night Slash, because then you could abuse a 100% Crit Rate Sucker Punch. And no, no added benefits from Pokemon Amie affect online battles, it would be too unbalanced.

Edit: Appears I made a mistake. Crit ratio is only increased from Stage 2 upwards, so actually, it would be 1/16 for a standard Pressure Absol, 1/8 for a Max Affection or Super Luck Absol, 1/2 for a Max Affection and Super Luck Absol, and 100% for a Max Affection, Super Luck and Crit Rate boosting item/High Crit move Absol. My apologies for the mistake, but my final point still stands, you can use Max Affection, Super Luck and Razor Claw to abuse a 100% Crit Hit Sucker Punch.